Intercellular communication in the brain through a dendritic nanotubular network

“ I fully admit that this is an appeal to authority! But saying you should rely on the framings of a scientific field, like literally just respecting how it defines terms, is extremely reasonable as an appeal. It’s also very different than saying you should blindly believe the conclusions of that field. While “trust the experts” is often too strong a claim, the much weaker ask of “use the agreed-upon vocabulary the experts use when discussing the field” is actually quite reasonable, and most people who want to have an opinion about a scientific (or philosophical) subject should respect the used terms. The same goes for consciousness.”

Walter Alvarez is another Nobel laureate who proposed a theory that an asteroid wiped out the dinosaurs. Many people thought that was crank science.

And it’s important to note he had another out there idea that there were hidden chambers in the pyramids of Egypt. That one turned out to be wrong.

What distinguished his theories from crank science is that he was open to the idea that they were wrong and was interested in actually using the scientific method to investigate them.

They will see that I accurately quoted what was said and my correspondent did not, twisting it into a circular argument when it wasn't.

As Penrose points out, the claim is conditional. Take a recursively axiomatized theory T for which we have Pi_1 soundness level warrant, i.e., we have reason to think its Pi_1 theorems are true in the standard model N for the arithmetical cases we care about. Then we can see (again: in N) that G_T is true while T cannot prove it.

That gives principled grounds to adopt Pi_1 reflection or otherwise step to a stronger T'. No infallibility claim about people is require. This mirrors the ordinary kind of warrant mathematicians use when they adopt new axioms after scrutiny and debate.

>A proof checker plus brute-force search can do Gödel reasoning, so a robot can do it.

A checker plus search enumerates exactly the theorems of whatever fixed system it’s tied to. You can also script computable progressions that iterate reflection or consistency along recursive ordinal notations in the Turing/Feferman style. That’s still a single computable progression determined in advance. It isn’t that such progressions don’t exist, but that our justified acceptance is not a priori bounded by any one fixed computable progression.

The mechanist reply here is an existence thesis: there exists some computable procedure whose output matches everything humans could in principle come to rightly endorse for arithmetic. If that’s your view, give the existence argument. If instead you propose a specific computable progression P that we could in principle ratify as Pi_1 sound in toto, Gödel/reflection immediately pushes past P. If you say we can’t justifiably ratify P as a whole, you’ve conceded the point that no single precommitted computable scheme captures the moving boundary of what we’re warranted to accept.

>Gödel didn’t show transcendence.

In the narrow sense above, Gödel shows how to go beyond any accepted, fixed rule set once we have Pi_1 soundness level warrant for it. That is exactly the move at issue. Note the scope: inside a system you can’t adopt “if provable then true” without collapse by Löb. Outside, adopting restricted Pi_1 reflection is the justified step. If you want to reject the move, reject the warrant. Deny that we sometimes justifiably regard a given fragment of T as Pi_1 sound for the cases at hand. That’s an objection about epistemic warrant, not a logic gotcha.

>Busy Beaver shows limits, so case closed.

Busy Beaver actually helps here. It yields concrete Sigma_1 statements that can be independent of strong base theories, illustrating that warrant-driven extensions are sometimes needed to settle specific instances.

Either sometimes we do have adequate Pi_1 level meta warrant for a theory T on the arithmetical claims we care about. In which case we can recognize G_T as true in N and rightly move to T', ensuring our recognitions outrun that fixed T. Or deny such warrant altogether, in which case you haven’t refuted the conditional. You’ve just changed the target to a weaker notion of “what we can recognize.” The “humans are unsound” line doesn’t touch that conditional, and “just use a checker plus search” doesn’t answer the challenge unless you can support the existence of a single computable theory or precommitted progression that captures everything we could in principle come to rightly accept for arithmetic.

I can speak to the general opinion of his logical arguments among logicians. And it is not just widespread consensus against. It is a widespread consensus that the argument is filled with basic logic errors that render it absolutely wrong.

As Hilary Putnam points out, Penrose's arguments are even worse than Lucas'. In particularly Penrose argues that no program that we can know to be sound, can simulate all our human mathematical competence. But our brains do not use a sound thinking process. Therefore a sufficiently good simulation of our brains that it can do mathematics, would also not be sound. Gödel's theorem is entirely silent on the potential capabilities of such unsound systems.

Furthermore LLMs provide a convincing demonstration that unsound simulations of us can have surprising levels of competence. ChatGPT regularly demonstrates both its competence and unsoundness. Sometimes at the same time!

The potential for unsound systems to demonstrate competence far beyond what most expected, is demonstrated by LLMs. Admittedly the current error rate is unacceptably high. But it demonstrates that what Penrose claimed to be mathematically impossible, may plausibly become real within our lifetimes. (Though, given how old Penrose is, not his.)

It is very unlikely that it can tell you “everything you need to know” or even everything that could possibly be useful.

Even if that were the case we have no way of knowing that or even supporting that with our current understanding. That takes that statement thoroughly outside of the realm of science and into philosophy.

>Unless there is a black hole or temperatures on par with the big bang going on within our brain, the standard model will tell you what you need to know

Do you think that if it were that simple, that a world renowned physicist would capable of doing the back of the envelope math?

Also do you think that if it were that simple that this world renowned physicist could consistently convince other world renowned physicists to engage with him beyond simple 1 paragraph rebuttals? To the point where they will write entire chapters in books published by him?

You may not find his argument convincing, but his arguments aren’t dismissed as crank science outside of edgy internet posts.

Colliders provide clean, high energy tests to pin down masses, spins, and couplings, and we already need them for open problems. A bio anomaly would set targets, not replace colliders.